obtenues en allouant al´eatoirement selon une distribution uniforme les an- tennes aux TXs et aux RXs. Si le canal d’interf´erence contient 12 antennes, le canal d’interf´erence est ´etroitement faisable et l’algorithme pour les sc´e- narios ´etroitement faisables est utilis´e. Avec plus de 12 antennes disponibles, chaque antenne additionnelle est exploit´ee par notre algorithme pour r´eduire la taille de l’information de canal n´ecessaire. On peut observer que notre approche r´eduit fortement la taille de l’information de canal, et cela mˆeme lorsque la configuration est ´etroitement faisable.
approche peut potentiellement ˆetre ´etendue `a de nombreux autres sc´enarios et contribuer `a rendre les r´eseaux sans fil plus efficaces.
Motivations and Models
Introduction
2.1 State of the Art for Transmitter Cooperation
2.1.1 Saturation of the Wireless Medium
Wireless communication has become essential to our lives in many ways, through a variety of services and devices ranging from pocket phones to laptops, tablets, sensors and controllers. The advent of multimedia dom- inated traffic poses extra-ordinary constraints on data rates, latency and above all spectral efficiency. In mobile networks, the demand for data rate has increased exponentially in the past decade. In 2012, the global mobile traffic was equal to 10 times the size of the entire global internet traffic in 2000 and it is expected that the global mobile traffic will continue its expo- nential increase to reach a tenfolds increase within the next 5 years [2]. In order to deal with the expected saturation of available resources in currently used bands, the architecture of the wireless networks and their transmission schemes have to be rethought. Key enablers for the strong performance of new wireless systems will be a i) greater densification of infrastructure equipments (small cells [3]), andii) a very aggressive spatial frequency reuse, which in turn results in severe interference conditions for cell-edge termi- nals. It has then become increasingly clear that the bottleneck of the future wireless networks will be the management of interference [4].
2.1.2 Downlink Multi-user Single-cell Transmission
In the last decade, an impressive number of works have been focused on the downlink transmission where one single transmitter (TX) serves mul- tiple receivers (RXs). In the information-theoretic community, this trans-
mission scenario is well known as the broadcast channel (BC) [5, 6]. This scenario has been heavily investigated both in the information theoretic society and in the industry, and is now relatively well understood. The capacity of the Gaussian multiple-input multiple-out (MIMO) channel has been obtained [7, 8] and shown to be achieved by a non-linear scheme called dirty-paper coding (DPC) in which the interference are subtracted on the TX side [9]. In addition, the performance of linear precoding has been eval- uated [10, 11] and it has become clear that linear precoding is a practically interesting transmission scheme with lower complexity than DPC but good performance. Efficient algorithms have also been developed in order to max- imize the performance with regards to different figures-of-merit while having a low complexity [12, 13]. However, the performance improvement can only be obtained at the cost of an accurate knowledge of the channel state at both the TX and the RXs [14, 15].
To translate these theoretic gains into practical performance, it has then been investigated how to estimate and feedback the channel state in realistic scenarios. Methods to obtain accurate feedback at the TX at low cost have been developed [16] while the impact of having imperfect channel state in- formation (CSI) at the TX has been evaluated [15]. It has also be shown how channel dependent scheduling could help improve the performance and make the transmission more robust to imperfect CSIT [17, 18]. A comprehensive study of multiuser-MIMO transmissions with linear precoding is provided in [19].
Even with the novel developed schemes, obtaining perfect CSIT remains unrealistic due to the changing nature of the channel. Therefore, trans- mission methods being more robust to imperfect CSIT have been provided, optimizing either the average performance over the CSIT errors [20] or op- timizing the worst case behavior [21, 22]. Another line of work aiming at exploiting delayed CSIT has been triggered by the work [23] where it was shown that even completely outdated CSIT (not correlated with the current channel state) could help improve the performance over a setting without CSIT. Since then, many works have study how to exploit delayed CSIT (See [24–26] among others).
Finally, using TXs with a very large number of antennas, so-calledmas- sive MIMO, has been recently advocated in [27] as a solution to improve further the performance while easing the requirements in terms of signal processing and CSI. It is now considered a promising method and is the focus of the research of an increasingly large community. It is investigated both by companies developing prototypes of such TXs and by the academic world (see [28–30], among others).
2.1.3 Multi-cell Processing
Although the progresses and innovations done regarding the single-cell trans- mission have lead to great performance improvements, they remain fun- damentally limited by the inter-cell interference. Thus, TX cooperation has appeared recently as the key to further performance improvements [4].
One conventional method to reduce inter-cell interference is by coordinat- ing resource allocation via flexible and coordinated scheduling. Different frequency allocations schemes have been proposed with the goal to adapt to the interference generated in order to improve the transmission effi- ciency [31–34].
Without user’s data sharing: Coordinated Beamforming (CB) The use of multiple-antennas at the TX offers additional opportunities for the TX cooperation. If each user is served only by one TX via linear pre- coding, it is possible to design the precoder (also called beamformer) so as to emit little inter-cell interference, so-calledcoordinated beamforming [39].
With a single-antenna at each RX, the coordination of the TXs can be done based on mostly local CSIT and efficients methods have been found to op- timize the precoder design or the feedback [40–48].
In contrast, with multiple-antennas available at the RXs, the transmis- sion paradigm changes completely. It becomes then possible to align in- terference at a restricted number of dimensions such that a RX can then suppress the remaining interference via RX zero forcing (ZF). This precod- ing scheme has been called interference alignment (IA) [37, 38, 49] and has lead to an impressive number of new algorithms (See [51–53] among others) and analysis (See [49, 50, 54], among others). In IA, the interference are ZF jointly at the TXs and the RXs which can lead to a strong improvement of performance. However, it requires a higher degree of coordination among the TXs since all the TXs have to agree on the RX dimensions in which all the interference are restricted. Hence, all the algorithms cited above require global CSI at every TX. Without data sharing between the TXs (i.e., among the coordinated beamforming techniques), IA represents the transmission scheme with the strongest potential and the higher feedback requirements. Hence, in the absence of user’s data symbol sharing, we will always consider that the RXs have multiple-antenna such that IA can be applied.
With user’s data sharing: Joint Precoding (JP)
When the user’s data symbols can be shared to several TXs via for exam- ple a backhaul network, it is then possible for one user to be served jointly by several TXs. This scenario whereby multiple interfering TXs share user messages and allow for joint precoding, denoted as “Network MIMO” or
“Multi-cell MIMO”, is currently considered for next generation wireless net- works [4, 55, 56]. With perfect message and CSI sharing, the different TXs can be seen as a unique virtual multiple-antenna array serving all RXs, in a multiple-antenna BC fashion. It is in fact clear that the cooperation through JP allows theoretically for the largest improvement as it requires more exchange of information between the TXs than the other alternatives.
A distinct advantage of TX cooperation over conventional approaches relying on egoistic interference rejection at the RXs, lies in the reduced number of antennas needed at each RX to ZF residual interference. This gain is further amplified when user data messages exchange among TXs is made possible. For instance, in the case of three interfering two-antenna TXs, relying on RX based interference rejection alone requires three antennas at each RX to ZF the interference, while just two are needed when coordination is enabled via IA. Further, if the three user messages are exchanged among the TXs, thus enabling JP, then just one antenna per TX and RX is sufficient to preserve interference-free transmission.